# SZS status Theorem
# SZS status Theorem
# SZS output start CNFRefutation.
fof(1, conjecture,![X1]:(![X2]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X1),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X1),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))))))))=>p(s(t_bool,h4s_bools_oneu_u_one(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X1))))),file('i/f/arithmetic/STRICTLY__INCREASING__ONE__ONE', ch4s_arithmetics_STRICTLYu_u_INCREASINGu_u_ONEu_u_ONE)).
fof(2, axiom,![X3]:![X4]:((p(s(t_bool,X4))=>p(s(t_bool,X3)))=>((p(s(t_bool,X3))=>p(s(t_bool,X4)))=>s(t_bool,X4)=s(t_bool,X3))),file('i/f/arithmetic/STRICTLY__INCREASING__ONE__ONE', ah4s_bools_IMPu_u_ANTISYMu_u_AX)).
fof(18, axiom,![X15]:![X12]:![X1]:(p(s(t_bool,h4s_bools_oneu_u_one(s(t_fun(X12,X15),X1))))<=>![X16]:![X17]:(s(X15,happ(s(t_fun(X12,X15),X1),s(X12,X16)))=s(X15,happ(s(t_fun(X12,X15),X1),s(X12,X17)))=>s(X12,X16)=s(X12,X17))),file('i/f/arithmetic/STRICTLY__INCREASING__ONE__ONE', ah4s_bools_ONEu_u_ONEu_u_THM)).
fof(21, axiom,![X2]:![X23]:(p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X2))))<=>(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X2))))|s(t_h4s_nums_num,X23)=s(t_h4s_nums_num,X2))),file('i/f/arithmetic/STRICTLY__INCREASING__ONE__ONE', ah4s_arithmetics_LESSu_u_ORu_u_EQ)).
fof(22, axiom,![X2]:![X23]:(~(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X2)))))<=>p(s(t_bool,h4s_arithmetics_u_3cu_3d(s(t_h4s_nums_num,X2),s(t_h4s_nums_num,X23))))),file('i/f/arithmetic/STRICTLY__INCREASING__ONE__ONE', ah4s_arithmetics_NOTu_u_LESS)).
fof(23, axiom,![X1]:(![X2]:p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X1),s(t_h4s_nums_num,X2))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X1),s(t_h4s_nums_num,h4s_nums_suc(s(t_h4s_nums_num,X2))))))))=>![X23]:![X2]:(p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,X23),s(t_h4s_nums_num,X2))))=>p(s(t_bool,h4s_primu_u_recs_u_3c(s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X1),s(t_h4s_nums_num,X23))),s(t_h4s_nums_num,happ(s(t_fun(t_h4s_nums_num,t_h4s_nums_num),X1),s(t_h4s_nums_num,X2)))))))),file('i/f/arithmetic/STRICTLY__INCREASING__ONE__ONE', ah4s_arithmetics_STRICTLYu_u_INCREASINGu_u_TC)).
# SZS output end CNFRefutation
